Proper SL(2,R)-actions on homogeneous spaces

Abstract

We study the existence problem of proper actions of SL(2,R) on homogeneous spaces G/H of reductive type. Based on Kobayashi's properness criterion [Math. Ann. (1989)], we show that G/H admits a proper SL(2,R)-action via G if a maximally split abelian subspace of Lie H is included in the wall defined by a restricted root of Lie G. We also give a number of examples of such G/H.

to appear in International Journal of Mathematics

References in corpus (2)

• Poincaré series for non-Riemannian locally symmetric spaces
• Clifford-Klein forms and a-hyperbolic rank

Cited by in corpus (1)

• Homogeneous spaces of real simple Lie groups with proper actions of non virtually abelian discrete subgroups: a calculational approach